New R-implication generated by T-partial order

A class of new implications derived from T-partial order, called R-implications, is introduced. The motivation originates from the idea that R-implication is generated by the t-norm and natural order. Whenever the supremum of those elements in the unit interval exists w.r.t. T-partial order, it is shown that each T-partial order induced by a t-norm T can yield an R-implication. Finally, one indicates that the generated R-implication fulfills the Modus Ponens property w.r.t. T-partial order.